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Total Internal Reflection
Before we can understand total internal reflection we must examine refraction and its properties: When monochromatic light travels from one medium into another, the speed the light wave changes. If the light enters a medium at an angle, it will change in direction as it passes into the second medium. The angle at which light travels through a medium is dependent upon the index of refraction of the medium. The index of refraction of a medium is the ratio of the speed of light in a vacuum (a vacuum is an environment without any interference) to the speed of light in the medium. The absolute index of refraction is always greater than or equal to 1. The larger the index of refraction, the slower the speed of light in the medium. For example, light travels faster in air than in diamond, we can assume this by examining their indices of refraction which are 1.00 and 2.42 respectively. We can predict the angle at which light will travel through a medium when it enters it coming from another medium with the help of Snell’s Law. Snell’s Law is as follows: n1 sin 1= n2 sin 2. The Normal Line: The normal line with respect to a plane is an imaginary line that runs perpendicular to the surface plane of the medium. The Critical Angle: When monochromatic light travels from one medium to another the angle at which it travels changes as it moves from one medium into another. There is one angle in medium one that will produce an angle of 90 degrees with respect to the normal line in the second medium—this is the critical angle. Therefore, building upon Snell’s Law, the equation for finding the critical angle is as follows: n1 sin c = n2 sin 90. Total Internal Reflection: When there is a critical angle between two media, this means that the refracted ray would skim the surface between the two media. Therefore, if the critical angle were exceeded, the light would be reflected back into the medium. Let’s prove this theory: Out two media will be air and flint glass:  Medium 1: Flint glass has an index of refraction (n) of 1.66  Medium 2: Air has an index of refraction (n) of 1.00 Finding the critical angle: n1 sin c = n2 sin 90 1.66 sin c = 1.00 1 sin c = (1.00/1.66)  = 38.68 Exceeding the critical angle: 1.66 sin 50 = 1.00 sin  1.27 = sin  ... this problem cannot be completed due to the fact that no value over 1.00 can equal sin . Therefore it follows that this law of refraction cannot work if the angle at which the light travels through the first medium into the second exceeds the critical angle. This means that the light is not refracted if the angle exceeds the critical angle—it is reflected and therefore follows the equation dictating how light behaves when reflected, ?i = r. ---- Applications of Total Internal Reflection: Diamonds: You can easily observe total internal reflection by examining how light is reflected within a diamond. Diamonds are cut so that light reflects off of its many sides back into the diamond and the light is only allowed to leave after many internal reflections, through the top, this gives the diamond its intense sparkle. Fiber Optics: A fiber optic is a very thin "hairlike" rod of glass, so thin that it is extremely flexible. In a fiber optic, light enters one end and because it is so thin, the light is never able strike the inside walls at less than the critical angle. This means that the light undergoes total internal reflection each time it strikes the wall of the fiber optic. Therefore, the light is only able to exit at the other end of the fiber. Fiber optic cables (bundles of fiber optics) are used to carry telephone and computer communications. Fiber optics are advantageous to the user because they can carry much more information in a much smaller cable, have no interference from electromagnet fields and this results in "clearer" connections, have no electrical resistance, and there is no hazard of electrocution if a fiber optic cable breaks.